Closer to our work is the line of research on manifold learning, a generalization of the classical field of linear dimensionality reduction to the nonlinear setting [1]}, [2]}, [3]}, [4]}, [5]}.
This line of works arises from the assumption that we observe the data in a high-dimensional Euclidean space \(\mathcal {X}\subset \mathbb {R}^N\)  sampled from a low-dimensional manifold \(\mathcal {M}\) , which can be approximately embedded into a low-dimensional Euclidean space \(\mathcal {Z}\) .
We make this assumption stronger, by conjecturing that the data manifold is factorizable into a product of subspaces; each subspace models a generative factor of the data.
